Heterogeneity in Distributed Live Streaming: Blessing or Curse?

Distributed live streaming has brought a lot of interest in the past few years. In the homogeneous case (all nodes having the same capacity), many algorithms have been proposed, which have been proven almost optimal or optimal. On the other hand, the performance of heterogeneous systems is not completely understood yet. In this paper, we investigate the impact of heterogeneity on the achievable delay of chunk-based live streaming systems. We propose several models for taking the atomicity of a chunk into account. For all these models, when considering the transmission of a single chunk, heterogeneity is indeed a ``blessing'', in the sense that the achievable delay is always faster than an equivalent homogeneous system. But for a stream of chunks, we show that it can be a ``curse'': there is systems where the achievable delay can be arbitrary greater compared to equivalent homogeneous systems. However, if the system is slightly bandwidth-overprovisioned, optimal single chunk diffusion schemes can be adapted to a stream of chunks, leading to near-optimal, faster than homogeneous systems, heterogeneous live streaming systems

On Resource Aware Algorithms in Epidemic Live Streaming

Epidemic-style diffusion schemes have been previously proposed for achieving peer-to-peer live streaming. Their performance trade-offs have been deeply analyzed for homogeneous systems, where all peers have the same upload capacity. However, epidemic schemes designed for heterogeneous systems have not been completely understood yet. In this report we focus on the peer selection process and propose a generic model that encompasses a large class of algorithms. The process is modeled as a combination of two functions, an aware one and an agnostic one. By means of simulations, we analyze the awareness-agnostism trade-offs on the peer selection process and the impact of the source distribution policy in non-homogeneous networks. We highlight that the early diffusion of a given chunk is crucial for its overall diffusion performance, and a fairness trade-off arises between the performance of heterogeneous peers, as a function of the level of awareness

Size Does Matter (in P2P Live Streaming)

Optimal dissemination schemes have previously been studied for peer-to-peer live streaming applications. Live streaming being a delay-sensitive application, fine tuning of dissemination parameters is crucial. In this report, we investigate optimal sizing of chunks, the units of data exchange, and probe sets, the number peers a given node probes before transmitting chunks. Chunk size can have significant impact on diffusion rate (chunk miss ratio), diffusion delay, and overhead. The size of the probe set can also affect these metrics, primarily through the choices available for chunk dissemination. We perform extensive simulations on the so-called random-peer, latest-useful dissemination scheme. Our results show that size does matter, with the optimal size being not too small in both cases

Convergence of the D-iteration algorithm: convergence rate and asynchronous distributed scheme

In this paper, we define the general framework to describe the diffusion operators associated to a positive matrix. We define the equations associated to diffusion operators and present some general properties of their state vectors. We show how this can be applied to prove and improve the convergence of a fixed point problem associated to the matrix iteration scheme, including for distributed computation framework. The approach can be understood as a decomposition of the matrix-vector product operation in elementary operations at the vector entry level.Comment: 9 page

On Spatial Point Processes with Uniform Births and Deaths by Random Connection

This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current configuration for some response function $f$. An equivalent view point is that each pair of points of the configuration establishes a random connection at an exponential time determined by $f$, which results in the death of one of the two points. We concentrate on space-motion invariant processes of this type. Under some natural conditions on $f$, we construct the unique time-stationary regime of this class of point processes by a coupling argument. We then use the birth and death structure to establish a hierarchy of balance integral relations between the factorial moment measures. Finally, we show that the time-stationary point process exhibits a certain kind of repulsion between its points that we call $f$-repulsion

Easy identification of generalized common and conserved nested intervals

In this paper we explain how to easily compute gene clusters, formalized by classical or generalized nested common or conserved intervals, between a set of K genomes represented as K permutations. A b-nested common (resp. conserved) interval I of size |I| is either an interval of size 1 or a common (resp. conserved) interval that contains another b-nested common (resp. conserved) interval of size at least |I|-b. When b=1, this corresponds to the classical notion of nested interval. We exhibit two simple algorithms to output all b-nested common or conserved intervals between K permutations in O(Kn+nocc) time, where nocc is the total number of such intervals. We also explain how to count all b-nested intervals in O(Kn) time. New properties of the family of conserved intervals are proposed to do so